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Universitat Konstanz

Fachbereich Physik

LehrstuhlProf. Dr. P. Leiderer

Laserinduced nanobubbles

Diploma thesis

presented by

Stefan Weber

Konstanz, 18th of June 2007

Erstgutachter: Prof. Dr. Johannes BonebergZweitgutachter: Prof. Dr. Thomas Dekorsy

Title: Setup for the time resolved extinction measurements at four wavelengths.

Zusammenfassung

Erstmals wurde an diesem Lehrstuhl das Blasenwachstum an nanoskopischen Grenz-flachen, genauer gesagt an den Oberflachen von Gold-Nanopartikeln in Wasser, unter-sucht. Deren plasmonische Eigenschaften stellten sich als ein sehr empfindlicherIndikator fur Veranderungen in den dielektrischen Eigenschaften in und um dasPartikel heraus. Durch die gleichzeitige Messung bei vier verschiedenen Wellen-langen konnte der Einfluss einer thermischen Anregung durch einen Laserpuls aufdie optischen Eigenschaften sowohl nahe der Plasmonresonanz (488 nm, 561 nm1

und 635 nm), als auch im Bereich der Interband-Absorption (405 nm) und der lang-welligen Flanke der Plasmonresonanz (660 nm) untersucht werden. Durch den Ver-gleich von zeitaufgelosten Extinktionsmessungen mit 50 nm und 80 nm Goldpartikel-Suspensionen mit Mie-Simulationen, die die makroskopischen, temperaturabhangigendielelektrischen Funktionen der beteiligten Materialien enthielten, konnte derMechanismus fur das Blasenwachstum um die Partikel abgeleitet werden.

Schon bei niedrigen Pulsenergien konnten Veranderungen in der Absorption derProben durch das Aufheizen von Partikel und Umgebung festgestellt werden (“lowfluence regime”). Das Ausbilden einer Dampfschicht an der Oberflache des Par-tikels bei hoheren eingestrahlten Fluenzen fuhrt zum Entkoppeln der plasmonis-chen Oszillationen vom umgebenden Dielektrikum, dem Wasser (“medium fluenceregime”). Dies fuhrt zu einem Abfall der Extinktion im sichtbaren Spektralbereich.Die Bildung einer Blase kann besonders gut im Signal des Abfragelasers bei 488 nmbeobachtet werden, da hier der Effekt des Aufheizens von Partikel und Umgebung (einAnstieg der Extinktion) genau entgegengesetzt zu dem Effekt der Blasenbildung ist.Mit steigender Fluenz des anregenden Lasers werden auch die Blasen immer großerund schließlich dominiert das Streuvermogen der Blasen die optischen Eigenschaftender Probe (“high fluence regime”). Die Extinktion zeigt das Verhalten, das man vonDampfblaschen in Wasser erwarten wurde: die kurzen Abfrage-Wellenlangen werdenstarker gestreut als die langen. Schließlich wird die Probe fur einige nanosekundenvollstandig undurchsichtig, sie zeigt ein “Optical Limiting”-Verhalten.

In einem weiteren Experiment wurde gezeigt, dass die Empfindlichkeit des Aufbausdurch die Verwendung von Abfrage-Wellenlangen nahe der Plasmon-Resonanz nochweiter gesteigert werden kann. Des Weiteren wurde die Wellenlange des Pulslasers

1Der Laser bei 561 nm kam nur fur eine letzte Messung zum Einsatz (vgl. Abschn. 4.5).

v

in den ultravioletten Bereich verlegt, da die Absorption hier weniger empfindlich aufVeranderungen im Partikel und seiner Umgebung reagiert. Die Wesentlichen Merk-male der vorherigen Messungen konnten reproduziert werden. Außerdem bestatigtesich die Vorhersage der Mie-Theorie, dass im grunen und gelben Spektralbereicherheblich starkere Signale zu erwarten sind.

vi

Contents

1 Introduction 1

2 Basic theory and state of research 32.1 Optical properties of metal nanoparticles . . . . . . . . . . . . . . . . 3

2.1.1 The quasistatic approximation . . . . . . . . . . . . . . . . . . 32.1.2 Mie theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Laser induced heating of gold nanoparticles . . . . . . . . . . . . . . . 62.2.1 The first picoseconds of a plasmon . . . . . . . . . . . . . . . 72.2.2 Heat conduction in and around the particle . . . . . . . . . . 82.2.3 Superheating and bubble nucleation . . . . . . . . . . . . . . . 10

2.3 Previous publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Experimental setup 15

4 Results and discussion 194.1 Optical extinction spectra . . . . . . . . . . . . . . . . . . . . . . . . 214.2 The low fluence regime . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3 The medium fluence regime . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 The high fluence regime . . . . . . . . . . . . . . . . . . . . . . . . . 284.4.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.5 Experiments with uv-excitation and a yellow probe laser . . . . . . . 32

5 Outlook 35

Summary 36

A Mie theory 39

B Temperature dependent optical constants of gold 43

vii

Contents

C One dimensional heat transfer 47

Bibliography 49

viii

1 Introduction

Nanoscopic matter sometimes acts completely different from bulk material. Thiseffect is very pronounced for metal nanoparticles. Bulk gold, for example, is yellowand shiny, whereas gold nanoparticles suspended in water show colours from darkred to pale orange, depending on size distribution and concentration. One of thefirst applications for these particles was in fact to give glass (e.g. in church windows)an intense red colour. Even from Roman times the use of metal nanoparticle dopedglasses was reported (see Fig. 1.1). These unique optical properties originate fromcollective oscillations in the electron gas of the particle, that lead to a highly increasedlight scattering and absorption. In the case of gold nanoparticles with diametersbelow 100 nm the absorption peak is in the green spectral range; hence the intensered colour.

What does this have to do with nanobubbles? Thanks to their absorption properties,metal nanoparticles can reach very high temperatures in a very short span of timeby pulsed laser irradiation. The subsequent heat dissipation can lead to a phasetransition in the surrounding matrix (e.g. water). This effect can be utilized fornumerous applications:

� Functionalized metal nano- and microparticles, that selectively bind to bio-logical structures such as tumours and other diseased cells or bacteria, can

Figure 1.1: The Lycurgus Cup is arichly decorated beaker that datesback to Roman times (fourth cen-tury AD). It depicts King Lycurgusof Thrace being dragged to the un-derworld. The glass appears green indaylight (reflected light) and red whenlight is transmitted from the inside ofthe vessel. These unique propertiescan be ascribed to scrap metal (goldin this case, see [Wag00]), that the Ro-man craftsmen habitually worked intothe glass in order to colour it.

1

1 Introduction

act as localized microabsorbers. The illumination with intense pulsed laserradiation leads to the creation of high peak temperatures that destroy thetargeted structures [Pit03, Lap06]. By using laser wavelengths that are stronglyabsorbed by the particles and not by the surrounding tissue, a highly localizedenergy deposition can be accomplished. The explosive formation of vapourbubbles around the nanoparticles then leads to the mechanical destruction ofcellular structures [Neu03, Neu05, Zha05].

� The scattering behaviour of the vapour bubbles can be used for the designof nonlinear optical devices. There has been an increased interest in effect ofOptical Limiting, i.e. on materials that remain transparent at low to moderatefluences and become opaque at a certain threshold fluence. In gold nanoparticlesuspensions, the formation of vapour bubbles following laser irradiation can leadto an increased scattering and finally the transmission is thoroughly suppressed[Fra00, Fra01].

� Rapid phase transitions following localized laser induced heating is a crucialissue for Steam Laser Cleaning. The efficient removal of microscopic con-taminations on sensitive surfaces, such as semiconductor or data storage de-vices, has become more and more important, as structures become smaller andsmaller. For Steam Laser Cleaning a thin liquid film is condensed onto thesubstrate and then irradiated with a short laser pulse. The energy absorptionin the substrate leads to a fast temperature increase both in the substrate and,due to heat transport, in the liquid film. Bubble nucleation at the solid-liquidinterface and the subsequent explosive vaporization of the liquid cause the re-moval of contaminants [Ime91, Zap91, Mos00]. This process can be seen an the“one dimensional version” of the Optical Limiting mechanism.

A number of previous works on Steam Laser Cleaning [Yav97, Mos00, Dob01, Lan02]and liquid-vapour phase transitions on planar surfaces [Yav94, Lan04, Lan06] gavethe motivation for this work. For the interpretation of these studies, an ideallyflat surface was assumed. The impact of surface roughness or contaminations asnucleation centres for the bubble formation has not been clarified satisfactorily, sofar. The aim of the present work is to study the bubble dynamics far away from asurface on defined “impurities”, viz. gold nanoparticles.

In the following chapter the basic principles of the optical properties of metal nanopar-ticles will be introduced. Furthermore, an overview over the basic mechanisms of theheat transfer from the heated particle to the surrounding water layers will be given,followed by a collection of publications related to pulsed laser - nanoparticle interac-tion. After a brief explanation of the experimental setup in Chapter 3 the results ofthe experiments and their interpretation will be given in Chapter 4.

2

2 Basic theory and state ofresearch

2.1 Optical properties of metal nanoparticles

The optical properties of gold nanoparticles in the visual spectral range are dominatedby collective excitations of the conduction electrons called plasmon polaritons orsimply plasmons1. They can be induced by external electromagnetic waves. In thefollowing sections a simple electrostatic model for plasmonic oscillations in metalclusters will be derived and the exact electrodynamic calculation for the Problem,the Mie-theory, will be introduced.

2.1.1 The quasistatic approximation

The response of a metal sphere of radius R in an external electric field is well knownfrom standard textbooks [Jac99]. The polarizability α links the polarization ~P of the

sphere to the external electric Field ~E0 by

~P = α ~E0 with α = 4πε0R3 ε− εmε+ 2εm

, (2.1)

where ε and εm are the static dielectric constants of the sphere and the surroundingmedium, respectively.

This result from classic electrodynamics also applies to a very small metal sphere inan oscillating electromagnetic field (wavelength λ) under certain assumptions:

� λ� R: That implies a constant phase of the external electromagnetic field toany given time over the particle volume. This regime is called the quasistaticregime.

1The term surface plasmon is often used in connection with the optical excitation of metal clusters.Surface Plasmons, however, usually have a penetration depth of some ten to twenty nanometres; soin nanoscopic particles most of the electrons will participate in the collective motion of the plasmon.

3

2 Basic theory and state of research

� Excitations due to the magnetic field of the wave do not occur (i.e. the perme-ability µ = 1). For the visual spectral range and its high frequencies this is areasonable assumption.

� Instead of the static dielectric constant ε the frequency dependent dielectricfunctions ε(ω) of the bulk materials are used.

� The dielectric function εm of the medium is usually taken as a real constantthroughout the visible spectral range.

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0-4

0

4

YAx

isTitle

X A x is T itle

Y

++ +++

---

--

Figure 2.1: Schematic of dipolar plasmonexcited by an external electromagneticwave.

The polarization of the particle shows a resonance behaviour, when the denominatorin α (Eq. 2.1) takes its minimum:

|ε(ω) + 2εm| = min.

With a complex dielectric function ε(ω) = ε1(ω) + i ε2(ω) this can be written as

[ε1(ω) + 2εm(ω)]2 + [ε2(ω)]2 = min, (2.2)

Assuming that close to the resonance ε2(ω) is small (i.e. small damping) or that itsfrequency dependence is small (∂ε2/∂ω ≈ 0), the resonance condition is given by

ε1(ω) = −2εm. (2.3)

For small particles (R < 10 nm) this gives a good approximation of the resonanceposition. For larger particles the inner field distribution is no longer homogeneous andhas to be developed by multipole expansions. This is done in the Mie theory, whichwill be introduced in the next section. But also for very small clusters (R <1 nm)deviations from the quasistatic approximation arise. In this size range the bulkdielectric functions can no longer be used for several reasons; for example, the meanfree path of the electrons is limited by the particle dimensions; furthermore theinfluence of the surface compared to the volume becomes dominant. However, thegold spheres used in this work are in the size range above 10 nm, so the use of bulkdielectric functions for the calculations is justified. For a more detailed discussionof the intrinsic size effects of the optical properties of metal clusters the reader isreferred to Chapter 2.1 in [Kre95].

4

2.1 Optical properties of metal nanoparticles

2.1.2 Mie theory

In the beginning of the 20th century Gustav Mie gave a general solution to theproblem of a sphere of arbitrary size and material exposed to an electromagnetic wave[Mie08]. He formulated appropriate boundary conditions and applied the Maxwellequations using spherical coordinates and multipole expansions. Input parametersare the dielectric functions of the sphere and the adjacent medium and - in contrastto the quasistatic theory - the particle radius R. The most striking feature of thiswork is that it applies for a wide range of different applications. The scatteringbehaviour of macroscopic objects, such as raindrops under irradiation of radar rays,can be computed as well as the behaviour of microscopic colloidal systems exposedto visible light.

In the context of the Mie theory a set of equations for absorption, scattering andextinction cross sections (σabs, σsca and σext) can be derived. In this context, crosssection means that the intensity loss of a homogeneous parallel beam of light afterpassing one single nanoparticle equals the intensity loss by an ideally absorbing sur-face with a surface area of σ. This is either due to dissipative losses (σabs) or due toelastic scattering (σsca) with the total loss being σext = σabs + σsca. In a system witha number density n = N/V of particles, the intensity loss ∆I(z) is given by

∆I(z) = I0 · (1− exp(−nσext · z)) (2.4)

Such a behaviour is often called a Lambert-Beer law. Although the Mie theory givesan exact solution to the problem, its formalism is lengthy and explicit calculationsare very time consuming. Nowadays this is mostly done numerically by computerprograms. In the present work the freeware program “MiePlot” [Lav06] was used tocompute spectral cross sections. The basic ideas of the mathematical formalism aregiven in Appendix A.

However for the quasistatic regime (R� λ) multipole orders higher than the dipolecan be neglected and the Mie formulas are simplified considerably. The extinctioncross section is in this case given by:

σext(ω) =9ω

cε3/2m V0

ε2(ω)

[ε1(ω) + 2εm]2 + [ε2(ω)]2(2.5)

The maximum of extinction is reached when the denominator takes its mini-mum. This leads to a resonance condition that is already known from Eq. (2.3):ε1(ω) = −2εm. Furthermore, the influence of the surrounding medium can be studied.

If the sphere material acts like a Drude metal with ε1 ≈ 1− ω2p

ω2 (i.e. ε1 is monotoni-cally growing with respect to the frequency; ωp is the plasma frequency), an increasingεm leads to a redshift of the plasmonic peak extinction.

5


400 500 600 700 800 900 10000.00

0.02

0.04

0.06

0.08

0.10

cros

sse

ctio

n[µ

m2 ]

wavelength [nm]

ssca

sabs

sext

400 500 600 700 800 900 10000.00

0.01

0.02

0.03

cros

sse

ctio

n[µ

m2 ]

wavelength [nm]

sext

ssca

sabs

(a) (b)

dipole

quadrupole

Figure 2.2: Simulated spectral cross sections for gold spheres with (a) 80 nm and (b)160 nm diameter. For the larger sphere the dipole resonance is shifted to the red and anadditional peak associated with the quadrupole resonance appears. Spectra generatedwith MiePlot [Lav06].

Some results of numerical calculations for goldparticles suspended in water are givenin Fig. 2.2. The plots show that for smaller particles (80 nm diameter) the dipolarmode is very pronounced. When the particle radius is increased, this mode is broad-ened and shifted to the red. Additionally, a second peak appears around 550 nm,which can be ascribed to the quadrupole resonance. The extinction plateau on theshort wave side of the resonance can be explained by interband transitions from thedensely populated d-band to higher conduction bands. The threshold for interbandabsorption in gold is at a photon energy of 2,4 eV to 2,5 eV (about 510 nm) [Kre95].

2.2 Laser induced heating of gold nanoparticles

In the last chapters the response of metal spheres to light irradiation was discussed,assuming that the absorbed energy does not cause any modifications in the particleor the surrounding water layers. For continuous wave irradiation the generated heatis dissipated fast enough to justify this assumption. Calculations show a temperatureincrease for a 100nm diameter gold particle in water being irradiated with a focused6 W, 532 nm (190 W/mm2) continuous wave laser of 10 K, which is negligible (seechapter 8.2 in [Dah06]). Pulsed lasers, on the other hand, can easily reach a power ofsome gigawatts for very short times. The processes coupled with the relaxation of thenon-equilibrium state after a laser pulse will be discussed in the following sections.

6


2.2.1 The first picoseconds of a plasmon

The dynamics in a metal nanoparticle following an ultrashort laserpulse has beenstudied very detailed in the past decade. In order to separate the different relaxationsteps, most studies used pico- or femtosecond laser pulses. With pump-probe ex-periments the changes in the optical transmission around the plasmon resonancepeak were observed with picosecond resolution (see for example [Har04]). From theresults of these studies the thermalization mechanism of the laser pulse energy in ametal particle could be inferred. It can be subdivided into three steps:

1. Excitation of the electron gasUsually the absorption of a laser pulse (with frequency ω) in noble metals isdue to intraband-absorption2. So electrons from the interval [εF − ~ω, εF ] belowthe fermi energy εF are excited to an interval [εF , εF + ~ω] leaving the electrondistribution in a non-equilibrium state. Via electron-electron scattering thesystem reaches a hot fermi distribution. For gold this thermalization processusually takes 500 fs [Fat00].

2. Energy transfer to the latticeDuring and after the equilibration of the electron gas, energy is being trans-ferred to the lattice by electron - phonon scattering. Typical relaxation timesfor gold are in the order of 1 ps [Fat01]. For the sake of completeness it shouldbe mentioned that the rapid increase in the lattice temperature and the corre-sponding expansion can excite vibrational modes in the particle with periodsaround ten picoseconds and damping times of 100 ps [Har06, Ple07].

3. Heat transfer to the matrixThe last step is the dissipation of the thermal energy into the surroundingmedium. In nanoscopic metal particles the surface area is found to have abig influence. Typical values for the cooling time τ in aqueous goldparticlesuspensions at low excitation powers are found to be in the order of 10 ps to380 ps for diameters ranging from 5 nm to 50 nm, τ being proportional to R2

[Hu02].

All these mechanisms are in the sub-nanosecond regime. The excitation in the ex-periments for the present work had been performed with pulse durations of 10 ns; sothe first two steps of thermalization should play no decisive role. Whether the laststep might become important will be discussed in the following section, where therelevant heat transfer mechanisms will be addressed in more detail.

2The lifetime of holes in the d -band caused by interband absorption is usually some tens of femtosec-onds in noble metals [Mat99]. Most of the recombination energy is transferred to the conductionband electrons, so assuming pure intraband absorption is feasible.

7


2.2.2 Heat conduction in and around the particle

The basic equation for diffusive heat propagation is given by:

∂T

∂t(~r, T )− κ∆T (~r, T ) =

A(~r, T )

ρcp, (2.6)

where A(~r, T ) is a heat source, ρcp is the volumetric heat capacity and κ the diffusionconstant or diffusivity of the material (see for example [Car59]). In most publicationsκ and cp are assumed to be temperature independent; for the materials used in thiswork this temperature dependence is in fact not very pronounced (see Appendix Ain [Neu05]). A convenient approach towards a solution of the problem is to use theGreenfunction of (2.6); i.e. the solution to the problem of a pointlike heat sourcewith infinitely short heating (A(~r, T )/ρcp = δ(~r)δ(t)):

g(~r,t) =1

8ρcp(πκt)3/2exp

(− r2

4κt

). (2.7)

The solution for an arbitrary temporal and spacial heat source A(~r, T ) is then ob-tained by convoluting it with (2.7).

For a rough estimation of the timescales for the equilibration of temperature differ-ences inside a inhomogeneously heated volume the time constant in the exponentialfunction of (2.7) can be used:

τeq =R2

4κ. (2.8)

For a spherical gold particle (κAu ≈ 1.2 · 10−4 m2/s) with 40 nm radius the ther-malization time is 3 ps. So with the excitation time for the experiments in this workbeing in the order of nanoseconds, a homogeneous temperature distribution insidethe particle can be assumed.

For the energy transfer to the surrounding water during a laser pulse (duration τL),the thermal diffusion length can be defined:

rth = 2√κW τL. (2.9)

For water (κW ≈10−7 m2/s) and a pulse duration of 10 ns, a layer of 75 nm radiusaround the heat source can be heated up until the end of the pulse. Of course, theserough approximations neglect some important aspects of the problem:

� The particle-fluid interfaceFor the heat conduction at an interface between different materials the heat

8


transmission resistance Rc is important. It can lead to a heat confine-ment inside the particle, that has to be considered in (2.6). The values fornanoscopic spheres can differ considerably from bulk materials and planar sur-faces. Approximate values for the thermal conductance coefficient from a metalnanosphere to water were given in [Wil02] and [Ple04]. They obtained a con-sistent value of G = 1/Rc ≈ 100 MW/m2K.

� Evaporation of the embedding mediumThe high temperatures in the particle give rise to a rapid heating in the sur-rounding layers of the matrix. If the timescale is short enough, the liquid phasecan be superheated and explosive boiling can occur [Kot06]. The formation of avapour bubble leads to a further heat confinement, as the thermal conductanceof steam is approximately a factor 40 lower than the thermal conductance ofliquid water.

� Melting and evaporation of the particleHeating metal nanoparticles by pulsed laser irradiation can easily lead to tem-peratures of some 1000 K inside the sphere [Pus06]. It has been shown that thiscan result in melting [Ple04] or even the complete destruction of the particles[Kur98, Lin00]. These phase transitions require additional energy in the formof latent heat.

� Radiative energy loss (a)The energy transfer over the particle boundary does not necessarily have to bedue to heat conduction only. Every surface that has a temperature above 0 Kis a source of thermal radiation according to the Stefan-Boltzmann law:

Pr = ε σ AT 4, (2.10)

where A is the surface area and ε the surface emissivity; σ =5.67 · 10−8 J/m2sK4

denotes the Stefan-Boltzmann constant.

� Radiative energy loss (b)Another possible radiative loss mechanism would be photoluminescence. It wasfirst discovered by Mooradian in 1968 on smooth gold surfaces [Moo69]. Therecombination of excited electrons from the conduction band with holes in the d-band give rise to a broadband light emission of the sample. Mooradian reporteda quantum efficiency of ∼ 10−10 for his experiments. Many groups reportedan increased efficiency on rough surfaces or on nanoparticles [Boy86, Bev03,Wil98], which suggests a plasmonic contribution to the effect. The emittedradiation in their experiments is mainly in the red and infrared spectral range.Wilcoxon et. al. found the quantum efficiency for gold nanoclusters particlesto be in the order of 10−4 − 10−5. Yet, these efficiencies are much too low togive any significant contribution to the energy loss of the particle.

9


For a liquid gold surface (emissivity ε ≈ 0.3 [Kri90]) at a temperature of 3000 K theenergy flux is J ≈ 1.4 MW/m2. However, thermal conductance of the metal-waterinterface is many orders of magnitude larger and even the thermal conductance ofa 100 nm steam layer around the particle would be in the order of Jc ≈ K∆T

∆r≈

500 MW/m2 (thermal conductivity of steam K = 0.016 W/m · K). Hence, the energyloss caused by radiation can be neglected. Whether the emitted radiation mightbecome important for the optical signals will be discussed in Sec. 4.4.2.

2.2.3 Superheating and bubble nucleation

During the process of laser induced heating of nanoparticles, the surrounding fluid caneasily reach temperatures far above the boiling temperature for the ambient pressure.The timescales of heating being very short, the boiling may not start instantaneously.Instead, a metastable phase can form, followed by explosive evaporation of the liquid.The liquid-gas phase transition can be described within the scope of the van der Waalsmodel. A van der Waals isotherm at a temperature T below the critical temperatureTc is shown in Fig. 2.3. On the left hand side of the diagram the substance isa pure liquid, on the right it is a pure gas; between the points A and E vapourand liquid phase coexist. The dashed lines denote the limits of metastable states,where the substance can still exist as pure liquid/vapour. The inner line is calledthe spinodal; underneath this line (between B and D) the material is intrinsicallyunstable, as

(∂P∂V

)T> 0. The upper temperature limit for the coexistence of liquid

and vapour is the critical temperature Tc. Above Tc the pressure p(V ) is found tobe monotonically decreasing with respect to V , that is, the substance is in a gaslikestate called supercritical fluid. 2.2 Liquid-Vapor Phase Transitions

Figure 2.4: P-v phase diagram for the liquid vapor transition. The solid line represents anisotherm for T < Tc. The horizontal line is placed according to the Maxwell constructionso that it confines areas of equal size with the isothermal line.

the isotherm are of equal size. The saturation curve is found, by constructing the

outer intersection points A and E for different isotherms. It is also known as the

binodal curve and defines, where the phase transition occurs in thermodynamical

equilibrium. Nevertheless, starting from the liquid phase the isotherm can be fol-

lowed beyond the point A after which the liquid becomes metastable. At the point

B the mechanical stability criterion − (∂P∂V

)T,N

> 0 fails and therefore the limit of

metastability is reached. It should be noted that five more stability criteria ex-

ist((

∂T∂S

)P,N

> 0 ,(

∂T∂S

)µ,V

> 0 , − (∂P∂V

)µ,S

> 0 ,(

∂µ∂N

)P,S

> 0 ,(

∂µ∂N

)T,V

> 0)

and

that all of them fail simultaneously [Deb96]. Similarly, the binodal can be passed

at the point E starting from the vapor phase until the point D is reached. The

entire spinodal curve is found by determining the points B and D for different

temperatures. In the following discussion spinodal refers to the part of the curve

left of the critical point, which is denoted as the liquid spinodal in Fig. 2.4, since

this is the relevant part for the liquid-vapor phase transition.

Fig. 2.5 shows the saturation curve and the spinodal for the liquid-vapor transi-

tion in a schematic P-T-phase diagram. The kinetic limit of superheating indicated

in the diagram will be discussed in Section 2.2.2.2. A liquid is superheated, if its

9

Figure 2.3: P-V diagramfor the liquid vapour tran-sition [Lan06].

10

2.3 Previous publications

Typical values for the lifetime of a superheated liquid in laser-heated systems havebeen investigated in connection with Steam Laser Cleaning experiments. Lang cal-culated the temperature behaviour at a planar silicon isopropanol interface uponirradiation with a Nd:YAG pulse [Lan06]. He found that the liquid is in a metastablestate for 1.4 ns before bubble nucleation sets in. Of course, these results cannotbe transferred directly to the three dimensional situation of a sphere in water. Thesurface-to-volume fraction is much higher in the three dimensional case and the evap-orating liquid has more degrees of freedom for its expansion. Hence, the timescalesfor the boiling retardation should be smaller. In fact, Plech and coworkers foundbubble nucleation by femtosecond excitation to set in after less than 1 ns [Kot06].


Several groups have been studying the interactions of pulsed lasers with metalnanoparticles in the past decade. Many of them used gold nanoparticles due totheir resonance behaviour in the visible spectral range (see section 2.1.2). A beau-tiful experiment was performed by Hartland and coworkers. They carried out timeresolved optical pump probe spectroscopy with a femtosecond Ti:Sapphire system.They used a small fraction of the pump beam and an adjustable delay line to gen-erate a white light continuum probe pulse at a sapphire window. Figure 2.4 showsthe result for 40 nm goldspheres in water. Immediately after the laser excitationthe extinction around the plasmon resonance (∼ 525 nm) is decreasing dramatically,while it increases in the wings of the resonance. The bleaching signal shows a strongdrop in the first ten picoseconds followed by a slower decay. The first drop is beingascribed to changes in the occupation of electronic states near the Fermi level fol-lowing the excitation; the further signal is caused by the slower heat transfer to theenvironment. The shape of the absorption signals can be described by changes in thedielectric functions due to the excited electrons and the following lattice expansion[Har06].

Optical spectroscopy is a very powerful tool for studying electronic properties of thematerials involved. However, structural changes or phase transitions are difficultto probe. Plech and coworkers focussed on time resolved x-ray scattering experi-ments with gold nanoparticle suspensions after femtosecond excitation. The heatingand melting of the particles could be observed [Ple04] as well as the bubble forma-tion around the spheres [Kot06]. For gold particles (diameter 35 nm) they found amaximum bubble lifetime of 2 ns at a fluence of 2000 J/m2 and estimated a maximumbubble volume of 140 times the particle volume. Additionally, threshold fluences forthe respective processes were ascertained by varying the excitation power.

For time resolved experiments pump-probe setups are very useful. However, it is verylaborious to get a sufficiently high temporal resolution over a longer span of time,

11


Figure 2.4: Time and wavelength resolved transient absorption change for goldparticles of∼40 nm diameter suspended in water. Top right: cross sections at different delay times;lower right: temporal evolution of the signal at two wavelengths. The vibration of theparticle following the rapid heating of the particle can clearly be seen as oscillation at547 nm [Har04].

as for every time step an individual measurement has to be performed. Anotherapproach would be to probe the transmission continuously at single wavelengths.Thus, the temporal evolution of the signals can be studied even for very long delaytimes. Inasawa and coworkers recorded the transmission signals for a 488 nm argon-ion laser and a 635 nm diode laser after irradiating 36 nm diameter goldparticles witha 30 ps third harmonic Nd:YAG laser pulse [Ina06]. They found short term absorp-tion changes on a timescale shorter than 50 ns on both wavelengths and permanentchanges on the red signal on a timescale of microseconds, which they explain by melt-ing and evaporation of particles. TEM studies show that in addition to the primaryparticles small clusters of some nanometres had appeared.

The mechanisms of size reduction and shape changes of metal nanoparticles due topulsed laser irradiation have also been studied. Kurita and coworkers observed thedestruction of gold particles by a second harmonic Nd:YAG at a repetition rate of10 Hz after several minutes. Size reductions of some ten nanometres were reported[Kur98].

12


with shape transformation and size reduction, respectively, wereobserved. Here, nanosecond time scales and longer are usedbecause it is hard for the widely used pump-probe method toobserve transient absorption on such long time scales and fewstudies have been done on these time scales. The transientabsorption of optically excited gold nanoparticles was observedat two different wavelengths, enabling us to gain a betterunderstanding of what causes the change in absorbance.

2. Experimental Section

An aqueous solution of gold nanoparticles was prepared usinga chemical reduction method, and the details are describedelsewhere.3,15,17,31The atomic concentration of gold used was0.12 mM, and the mean diameter of the nanoparticles was 36nm. The gold nanoparticles were excited using the thirdharmonic of an Nd:YAG laser (EKSPLA, PL2143B) (λ ) 355nm, pulsed width) 30 ps), irradiated through a 2 mmdiameteraperture. The fluence of the pump pulses was measured usinga power meter (Scientech, Model 362). Two continuous wavelasers of 488 nm (National Laser Company, 800BL) and 635nm (Sigma Koki, LDU33) wavelength were used as probes,having diameters of 1 mm or less. The probe laser lightirradiated through the excited area of solutions was detectedusing a Si PIN photodiode (Hamamatsu, S3883), and the signalswere amplified and recorded with an oscilloscope (SonyTektronix, TDS360). A sharp-cut filter (Suruga Seiki, S79-L39)was placed in front of the photodiode to cut UV light shorterthan 370 nm. To observe the dynamics induced by a single laserpulse, the solutions were flowed continuously through a quartzcell with an optical path of 5 mm.

UV-vis spectra were recorded on a multichannel detector(Hamamatsu, PMA-11) equipped with a white light source(Hamamatsu, L7893). A 50µL volume of an aqueous solutioncontaining 0.06 mM gold atomic concentration was placed intoa quartz cell (2× 10 × 45 mm3, optical path 10 mm), andspectra were obtained before and after irradiating with a singlelaser pulse (355 nm).

Gold nanoparticles were directly observed using a transmis-sion electron microscope (TEM) (JEOL, JEM-2010). A dropof the aqueous gold nanoparticle solution was deposited onto acarbon-coated TEM copper grid, which was then left to dry atroom temperature. After drying, the carbon grids were washedwith Milli-Q water to remove any remaining ionic precipitations.

3. Results

UV-vis spectra of the sample solution before and after thesingle pulsed laser irradiation are shown in Figure 1. Irradiationwith fluences of 15 or 30 mJ cm-2 produced an absorption dueto the surface plasmon resonance (SPR) of the gold nanoparticlescentered around 520 nm. This absorption showed a clear shiftto shorter wavelengths, as well as a weakened peak intensity,

compared to the initial spectrum. These changes in absorptionare consistent with previously reported work,3,4,14,15,17indicatingthat laser-induced shape transformation or size reduction of thegold nanoparticles has occurred. Irradiation of the sample withlaser energy of 30 mJ cm-2 produces a slightly strongerabsorption in the red region than that with energy of 15 mJcm-2. The identification of this absorption is discussed later.Absorbances below 500 nm showed little change because theabsorption originated in the interband transition (5df 6sp),32

which is insensitive to the size and shape of the nanoparticles.9,13

Figure 2 shows typical transient absorption spectra forirradiated gold nanoparticles obtained at 488 and 635 nm onthe nanosecond time scale. Irradiation with a laser energy of15 mJ cm-2 produced a sharp decrease in absorbance at 488nm (Figure 2a), suggesting that the gold nanoparticles becametransparent due to photoexcitation. The negative signal decayedfaster than the 5 ns time resolution of the experimental system.At 635 nm, however, the absorbance decreased instantaneouslyand remained constant for 300 ns (Figure 2c). A more intensepulse of 24 mJ cm-2 produced positive absorbance changes atboth wavelengths (Figure 2b,d), which were observed to decayquickly over a 5 nstime scale. The contrasting sign of the peaksignal in the transient absorption is a good indication thatdifferent phenomena occur with high laser intensity. With thelarger fluence (24 mJ cm-2), the observed absorbance after theinstantaneous decrease at 635 nm also remained constant (Figure2d). As an intermediate signal between the positive and negativepeaks shown in Figure 2a,b, both peaks were observed at thesame time with a laser fluence of 22 mJ cm-2 (Figure 3). Thesignal appeared to be the summation of both negative andpositive peaks (Figure 3), indicating that both phenomenaoccurred at this fluence. This intermediate signal was onlyobserved for a fluence of 22 mJ cm-2.

The values of the peak signals (∆Apeak) in Figure 2 wereplotted in Figure 4. At 488 nm,∆Apeak was found to decreasewith increasing laser fluence up to around 18 mJ cm-2. Abovethis fluence, in turn,∆Apeak increased as the fluence increasedand changed in sign above 24 mJ cm-2 (Figure 4a). The insetin Figure 4a shows negative values of∆Apeakat 488 nm in thelow fluence region. They decreased almost linearly above thethreshold energy of 6.3 mJ cm-2 (Figure 4a). At 635 nm, no

Figure 1. Absorption spectra of gold nanoparticles before and after asingle pulse of laser irradiation (355 nm).

Figure 2. Typical transient absorption spectra at 488 and 635 nm onthe nanosecond time scale. Irradiated laser fluences of 15 mJ cm-2 for(a) and (c) and 24 mJ cm-2 for (b) and (d) were used.∆Apeakrepresentsthe value of the peak signal in the measured transient absorption, and∆Abasemeans the difference in the absorbance at 635 nm, before andafter laser irradiation.

Laser-Induced Phase Transition of Au Nanoparticles J. Phys. Chem. B, Vol. 110, No. 7, 20063115

Figure 2.5: Typical transient absorption data from [Ina06]. (a) and (c) were recorded ata laser fluence of 15 mJ/cm2 and (b) and (d) at 24 mJ/cm2.

13

3 Experimental setup

For the experiments, gold colloid suspensions from British Biocell International (BBI)with particle diameters of 50 nm and 80 nm1 were used. Goldparticles in this sizerange were chosen due to their optical properties in the visible spectral range (seechapter 2.1.2), viz. the dipolar resonance in the range around 540 nm. Before andafter every experiment optical extinction spectra were recorded with a spectrometer(IKS Optoelectronic/Polytec X-dap).

For the optical measurements glass cells made of special optical glass (Hellma) wereused. The light path inside the cells was 2 to 10 mm. Initial studies have beenperformed with the larger cuvettes. Thanks to the increased probe volume, strongersignals are obtained. On the other hand the filled cuvettes have absorption ratesof up to 95%. Thus, the Nd:YAG intensity on the back of the cell is much lowerthan at the front. Consequently, the probe signals only provide an integral signal forthe different laser fluences in the probe volume. To avoid intensity gradients eitherthe particle suspensions can be diluted or the optical path length can be decreased.The advantage of the second option is, that due to the reduced probe volume lateralintensity gradients caused by the gaussian beam profile of the Nd:YAG beam can bediminished.

The setup for the time resolved absorption measurements is shown in Fig. 3.1. Thepulselaser source was a Q-switched, seeded Nd:YAG system (Continuum Powerlite),that can be operated with a second and a third harmonic generator, the outputwavelength being 532 nm (green) and 355 nm (ultraviolet), respectively. The tem-poral pulse form can be approximated by a gaussian with a pulse duration of 10 nsFWHM. The pulse energy was controlled by shifting the time between the ignition ofthe flash lamp and the activation of the Q-switch (Q-swich delay time). A drawbackof this method is an increase of the pulse duration towards low energies (either toolow or to high Q-switch delay times) of some nanoseconds.

Most experiments were performed with the second harmonic Nd:YAG. The advan-tage of the green laser pulses is the increased absorption of the gold spheres due tothe proximity to the plasmon resonance. However, further analysis showed that theexact position and the shape of the resonance peak is very sensitive to temperature

1The manufacturer specifies the deviations from the mean diameter to be less than 8% and theparticles to be more than 95% spherical.

15


Nd:YAG532nm / 355nm

beam expander1.5x - 2.5x

energymeter

PD

pbe a

r

rol se

oscilloscope

beam dumpand trigger PD

glass cellwith gold particles

Figure 3.1: Setup of the time resolved absorption measurement. The Nd:YAG beam isexpanded, ensuring a homogeneous illumination in the probe volume. A small fractionof the beam is deflected by a glass slide in order to determine the energy of the pulsewith an energy meter. Changes in the intensity of the probe beams (only one depictedhere) are monitored by a photodiode (PD) and an oscilloscope.

changes both in the particle and in the surrounding water layers. Hence, the absorp-tion coefficient may change during the laser pulse. In the ultraviolet spectral rangethe absorption is dominated by interband transitions and hence less affected by thetemperature of the system. The disadvantages of the ultraviolet beam are a lowerconversion efficiency in the third harmonic generator and a decreased stability of thepulse energy.

In order to assure a homogeneous illumination of the particles the beam is ex-panded by a confocal combination of a biconcave (f1 =−100 mm) and a biconvex(f2 =150 mm) lens. This configuration with a beam expansion factor of 1.5 hasproved to be a good compromise, providing a constant intensity over the whole probevolume at sufficiently high fluences.

-20 -10 0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

inte

nsity

[a.u

.]

time [ns]

CH1n (405nm) CH2n (488nm) CH3n (635nm) CH4n (660nm)

Figure 3.2: Synchronization of thesignals. The position of theNd:YAG pulse was recorded si-multaneously with all four photo-diodes; deviations of the peak po-sition are below 1 ns.

16

The extinction of the gold suspensions was probed at four wavelengths simul-taneously. On the shortwave side of the plasmon resonance (cp. Fig. 2.2 on page 6)a 405 nm diode laser (Oxxius Violet) was used to probe the response in the interbandabsorption regime. In the the spectral vicinity of the plasmon peak, an argon-ionlaser (Coherent Innova 90) at 488 nm and a diode laser at 635 nm were used. Finally,an additional diode laser at 660 nm was used to probe the red spectral range in theshoulder of the plasmon peak. In a last experiment the 660 nm laser was replacedwith a 561 nm continuous wave Nd:YAG2 , whose wavelength is very close to theplasmon resonance of the 80 nm particles.

All four beams were focussed on the same point in the cell and transmission changeswere monitored by photodiodes (FND-100Q, rise time ≈ 1 ns) and by a fast oscillo-scope (Tektronix TDS684B, 1GHz 5GS/s). In order to ensure a linear response ofthe photodiodes, the probe lasers intensities were equalized to a static photodiodesignal of 50− 60 mV. For the data analysis, an exact synchronisation of the signalsis vital, as deviations in the lightpath of 10 cm already give rise to a signal shift of1 ns. Therefore the same lightpaths and cablelengths were chosen for all wavelengths(Fig. 3.2). The Nd:YAG pulses were eliminated from the signals by appropriate edgeand interference filters. Thanks to the relatively big sensitive area of the photodiodes(5.1 mm2) signal changes due to thermal modifications of the refractive indices dur-ing the Nd:YAG pulse can be avoided. In order to decrease the effects of the noisefrom the lasers and the photodiodes the signals were averaged over 20-50 excitationpulses. During the measurement the Nd:YAG-pulse energies were sufficiently stable.In between the pulses there was enough time for the excess heat to diffuse from theprobe volume. At higher excitation fluences the cell was stirred after every pulse inorder to increase heat diffusion and to replace damaged particles.

Figure 3.3: Energy calibrationgraph for 532 nm. The laser flu-ence at the probe volume canbe approximated by a logarith-mic fit function (straight line).

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Data: Messung1_BModel: Log3P1Equation: y = a - b*ln(x+c)Weighting: y No weighting Chi^2/DoF = 95.72718R^2 = 0.9993 a -3402.47451 ±145.6462b -655.73109 ±20.50446c 182.20423 ±12.5437

lase

rflu

ence

atce

ll[m

J/cm

²]

deflected energy [µJ]

2The Nd:YAG laser is operated at the 1122 nm line and intra-cavity frequency doubled. A test laserwas kindly provided by Coherent Germany

17


A very important part of the experiments is the energy calibration of the excitationlaser. In order to determine the laser flux at the probe volume a copper plate witha pinhole was placed at the focus of the probe beams. Both the transmitted energybehind the pinhole and the reflection of a glass slide placed in the Nd:YAG beambefore the cell (see Fig. 3.1) were recorded with two energy meters (Coherent Field-Master GS with a Pulsehead LM-P2). The energy calibration curve for the 532 nmlaser is shown in Fig. 3.3.

18

4 Results and discussion

For the further interpretation it is vital to define some quantities related to thedata recorded in the experiments. The photodiodes are being operated in the linearresponse regime. Hence, the signals are proportional to the power of the incidentradiation I. The transmittance T of an object is defined by

T =I

I0

, (4.1)

I and I0 being the transmitted and the initial power, respectively. So the signalsfrom the photodiodes are a direct measure for changes in the transmittance of thesample. The absorbance is given by

A = − log10 (T ) = log10

(I0

I

). (4.2)

It depends on the substance and the layer thickness. As a geometry independentmeasure of the absorption properties of a substance, the optical density is defined bynormalizing the absorbance by the length l of the light path through the sample:

OD =A

l=

1

llog10

(I0

I

). (4.3)

If the sample has an extinction behaviour following a Lambert-Beer law (see formula2.4 on page 5), the transmittance of a layer with optical path length l can be writtenas

T (l) =I

I0

= exp(−σn · l)

⇒ − lnI

I0

= αA(l) = σn · l, (4.4)

where σ is the extinction cross section and n the number density of particles;α = ln 10 ≈ 2.3 is the correction factor for the decadic logarithm1.

1The decadic logarithm is conventional way to express A and OD in spectroscopy. However, thequantitative description requires the natural logarithm.

19


0 20 40 60 80 100-20

-10

0

80

60

40

20

0

time [ns]

D opt. density

[m-1] laser fluence

[mJ cm-2]

(a)

(b)

Figure 4.1: Overview over the energy dependence of the extinction signals for a 80 nmgoldparticle suspension at 488 nm. A small increase in optical density (a), visible at lowexcitation fluences (low fluence regime), is being superimposed by a strong drop (b) athigher fluences (medium fluence regime). The high fluence regime could not be assessedin this measurement (see Sec. 4.4).

Hence:

⇒ OD ∝ σ ·n, (4.5)

Changes in the optical density are directly proportional to changes in the extinctioncross section, assuming that the particle concentration remains constant.

It should be stressed at this point that these quantities do not include any informationabout the loss mechanism. The losses in the transmitted beam can be caused byabsorption processes as well as by scattering. So an increase in the optical densityof the sample does not necessarily imply that more heat is being generated insidethe sample. Therefore, the term extinction will be used to describe changes in thetransmitted intensity of the probe beams (see also Sec. 2.1.2).

For a better understanding of the optical density changes described in the subsequentsections, the static extinction spectra will be discussed in the next section. It turnedout that the optical response of the samples showed distinctive features at differentexcitation fluences as it can be seen in Fig. 4.1. At a probe wavelength of 488 nm theoptical density in the 80 nm goldparticle suspension showed a small increase at lowexcitation fluences (low fluence regime), followed by a strong drop at higher fluences(medium fluence regime). Hence, the description of the signals will be divided into thelow, medium and a high fluence regime. All experiments described in the followingthree sections have been performed with a excitation wavelength of 532 nm. Every

20

4.1 Optical extinction spectra

section will contain a presentation of the results and will be followed by a discussionand interpretation of the signals. Finally, first results of experiments with a yellowprobe laser (561 nm) and ultraviolet excitation (355 nm) will be presented.

4.1 Optical extinction spectra

Before and after every experiment optical extinction spectra of the samples wererecorded in order to search for irreversible effects caused by the laser irradiation.Plots for fresh particles and a comparison with the predicted extinction from the Mietheory are presented in Fig. 4.2. Using the particle density as a fit parameter, thetheoretical curves have been fitted to the same peak height.

The values for the density are in good agreement with the datasheet from the manu-facturer: For the 50 nm particles 5.9 · 1010 ml−1 are obtained (BBI: 4.5 · 1010 ml−1) andfor the 80 nm particles 1.0 · 1010 ml−1 (BBI: 1.1 · 1010 ml−1). The corresponding meandistances between neighbouring particles are 2.6 µm (50 nm) and 4.6 µm (80 nm).

In Table 4.1 the optical density values for the probelaser wavelengths are given to-gether with the corresponding transmission of the 2 mm layer of particle suspensionin the glass cells.

(b)(a)

400 450 500 550 600 650 7000

20

40

60

80

100

120

140

160 BBI EM.GC80 Mie theory

opt.

dens

ity[m

-1]

wavelength [nm]

400 450 500 550 600 650 7000

10

20

30

40

50

60

70

80

90

opt.

dens

ity[m

-1]

BBI EM.GC50 Mie theory

wavelength [nm]

Figure 4.2: Extinction spectra recorded before the excitation experiments for (a) 50 nm(BBI EM.BC50) and (b) 80 nm (BBI EM.BC80) goldparticle suspensions in a 2 mm cellcompared with the predicted curve from the Mie theory.

21


50 nm 80 nm

probelaser OD [ m−1] T2mm [%] OD [ m−1] T2mm [%]

405 nm 44 82 70 73

488 nm 48 80 67 73

561 nm 52 79 131 55

635 nm 12 95 37 84

660 nm 10 96 23 90

Table 4.1: Comparison of optical density and the corresponding transmittance of a 2 mmthick layer for the two goldparticle suspensions.

4.2 The low fluence regime

4.2.1 Results

In Fig 4.3 the optical response of 80 nm goldparticle suspensions at low excitationfluences is shown. Already slightly above the laser threshold of the Nd:YAG laser (i.e.5 mJ/cm2) a small increase in the optical density signal can be observed at 488 nmfollowing the excitation pulse. At a fluence of 8 mJ/cm2 the two wavelengths on thered side show an optical response in the opposite direction while the extinction at405 nm remains nearly constant (a small offset can be discerned in the noise). Theduration of the signals is about 20 ns; the response in the red wavelengths is shorterand comes with a small delay to the 488 nm signal. The signal form evolves from aninitially symmetric to an asymmetric shape with a rise time of 5 ns and a decay timeof 20− 25 ns. The signal amplitudes become stronger with increasing fluence until anadditional drop of some nanoseconds duration appears on the signal at 488 nm (see

0 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

1

time [ns]

Dop

t.de

nstit

y[m

-1]

660nm

5 mJ/cm²

488nm

405nm

635nm

higher fluence

0 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-1

0

1

time [ns]

Dop

t.de

nstit

y[m

-1]

660nm

8 mJ/cm²

488nm

405nm

635nm

Figure 4.3: Optical re-sponse of 80 nm goldparti-cle suspensions in the lowfluence regime. The curveshave been averaged over50 excitations. A changein the optical density of1 m−1 corresponds to atransmission change of0.5 %.

22

4.2 The low fluence regime

Figure 4.4: The upper graph clearlydemonstrates the asymmetry of thelow fluence signal at 488 nm (80 nmparticle suspension). The transition tothe medium fluence regime is markedby a short-term drop in the extinc-tion that becomes more and more pro-nounced towards higher laser fluences.

0 20 40 60 80 100 120 140 160 180 200-1

0

1

20 20 40 60 80 100 120 140 160 180 200

-1

0

1

20 20 40 60 80 100 120 140 160 180 200

-1

0

1

2

20 mJ/cm²

time [ns]

Dop

t.de

nstit

y[m

-1]

17 mJ/cm²

16 mJ/cm²

Fig. 4.4). The appearance of this signal at 17 mJ/cm2 marks the upper limit of thelow fluence regime. For the 50 nm particles it was not possible to obtain reproduciblesignals with a comparable structure at low excitation powers.

4.2.2 Discussion

When the goldparticles are irradiated with the laser pulse, a certain part of the lightis scattered and another part is absorbed (cp. Fig 2.2 on page 6). The absorbedenergy leads to a heating of the particle and the surrounding fluid. The asymmetryof the signal (upper graph in Fig. 4.4) suggests a rapid heating during the laser pulse,followed by a slower decay due to heat conduction to the environment.

The impact of the heating on the extinction properties can be simulated with MiePlotusing the refractive indices of bulk gold at 300 ◦C (from [Ott61], see also AppendixB) and the corresponding value for liquid water (n300 ◦C

W = 1.24 [Sch90]). The spectraand the corresponding signal changes are shown in Fig. 4.5. The simulations wereperformed at that particular temperature because the nucleation is reported to startaround 300 ◦C when using nanosecond excitation [Neu05]. The qualitative behaviourof the 80 nm particle suspensions, in particular the positive extinction change in488 nm can be reproduced. Therefore it is feasible to conclude that the opticalsignals reflect the temporal evolution of the temperature in and around the particle.The delayed onset of the response in the red probe beams might be explained bya different interaction range of the plasmonic oscillations with the red wavelengths“averaging” the temperature over a larger radius around the particle.

The cooling dynamics of gold nanoparticles following a sub-picosecond excitationhave been studied by Hu et. al. [Hu02]. For a 50 nm particle they found a coolingtime of 380 ps. If the trend of their data (a quadratic behaviour of the coolingtime with respect to the particle radius) is extrapolated to 80 nm goldspheres, a

23


(b) 80 nm gold particles in water

(a) 50 nm goldparticles in water

400 450 500 550 600 650 7000.00

0.25

0.50

0.75

1.00

in water 20°C in water 300°C

optde

nsity

[a.u

.]

wavelength [nm]

400 450 500 550 600 650 7000.00

0.25

0.50

0.75

1.00

20°C 300°C

optde

nsity

[a.u

.]

wavelength [nm]

400 450 500 550 600 650 700

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1D

opt.

dens

ity[a

.u.]

wavelength [nm]

405nm 488mn

561mn

635nm660nm

400 450 500 550 600 650 700

-0.4

-0.2

0.0

Dop

t.de

nsity

[a.u

.]

wavelength [nm]

405nm 488mn

561mn

635nm660nm

Figure 4.5: Simulated spectra for heated particles at 300 ◦C (left) and the correspondingsignal changes. The vertical lines indicate the wavelengths of the probe lasers.

cooling time of 1000− 1100 ps is obtained. However, the energies that are involvedin their experiments are much lower than the energies in the nanosecond pulsesused in this study. Moreover, the heating conditions for femtosecond excitation areadiabatic, whereas nanosecond heating means, that the particle will already heat upits environment during the laserpulse. Therefore, these timescales can be used as alower limit for the cooling times.

For an upper limit, the cooling times of a one dimensional simulation of the heatconduction can be used. The results of a calculation of a 80 nm thick gold layersurrounded by water and irradiated by a laserpulse are presented in Appendix C.The timescale for cooling is in the order of 100− 150 ns.

For the 50 nm particles the extinction changes are negative for all wavelengths andhence it is difficult to distinguish between low and medium fluence response.

24

4.3 The medium fluence regime

0 20 40 60 80 100 120 140 160 180 200

-4

-2

00 20 40 60 80 100 120 140 160 180 200

-4

-2

00 20 40 60 80 100 120 140 160 180 200

-8-6-4-20

0 20 40 60 80 100 120 140 160 180 200

-4

-2

0

time [ns]

Dop

t.de

nstit

y[m

-1]

660nm

51 mJ/cm²

488nm

405nm

635nm

0 20 40 60 80 100 120 140 160 180 200

-6-4-202 0 20 40 60 80 100 120 140 160 180 200

-6-4-202

0 20 40 60 80 100 120 140 160 180 200

-6-4-202

0 20 40 60 80 100 120 140 160 180 200

-6-4-202

time [ns]D

opt.

dens

tity

[m-1]

660nm

30 mJ/cm²

488nm

405nm

635nm

(b)(a)

Figure 4.6: Optical density signals for (a) 50 nm and (b) 80 nm particle suspensions.


4.3.1 Results

With increasing laser fluence the extinction drop shown in Fig. 4.4 becomes morepronounced. Fig.4.6 shows that the response closer to the plasmon peak (i. e.488 nm and 635 nm) is stronger than for the other wavelengths in the 80 nm particlesuspension. No significant changes in the the red probe beams could be observed forthe 50 nm particles, whereas the blue wavelengths show a behaviour that is similarto the response of the larger particles.

Again, the signals have an asymmetric shape. The red wavelengths and the 488 nmsignal show similar behaviour with short decay at a timescale of 5 ns and a recoverytime to the static extinction value of 20− 25 ns. The signal at 405 nm, however, hada relaxation time that was a factor four to five longer. Furthermore, the signal at635 nm did not fully recover to the static optical density value. This effect becomesstronger with increasing fluence and is stable for several milliseconds.

Another remarkable feature of the signal at 488 nm for the 80 nm particles is theinitial increase in optical density (black arrow in Fig. 4.6 (b) ), which is a residueof the signal at the low energy regime. The signal amplitude as a function of laserfluence is shown in Fig. 4.7.

25


(b)(a)

0 10 20 30 40 50 60 70

-15

-10

-5

0

0 10 20 30 40 50 60 70-6

-4

-2

0

laser fluence [mJ/cm2]

peak

Doptd

ensi

ty[m

-1]

488nm 405nm


660nm 635nm

0 10 20 30 40 50 60 70 80 90-15

-10

-5

0

0 10 20 30 40 50 60 70 80 90-2.0

-1.5

-1.0

-0.5

0.0


peak

Doptd

ensi

ty[m

-1]

488nm 405nm


660nm 635nm

Figure 4.7: Negative peak signal as a function of excitation fluence for the red (top) andthe blue probe lasers (bottom) in (a) 50 nm and (b) 80 nm goldparticle suspensions. Themore or less constant value of −0.5 m−1 for the red wavelengths in (a) can be ascribedto the noise of the laserdiode.

4.3.2 Discussion

With increasing laser fluence, more heat is dissipated into the adjacent water layers.Eventually, boiling sets in at the surface and a steam bubble forms around the parti-cle. This has two main consequences: first, the refractive index of the surrounding isdecreased and second, the heat conduction from the particle is decreased due to thelower heat conduction coefficient of steam.

The effect on the optical properties can be simulated with MiePlot. Again, thedielectric properties of gold at 300 ◦C from [Ott61] (cp. Appendix B) were used.The steam has a refractive index very close to unity [Sch90], so simulations wereperformed assuming vacuum around the particle. The spectra and the correspondingsignal changes are shown in Fig. 4.8. The vapour layer causes an extinction drop inall wavelengths with the strongest changes again being observed around the plasmonresonance. For the 50 nm particles only small changes in the red spectral rangeare predicted, which is confirmed by the experiment. The behaviour of the 80 nmparticles in the red spectral range are in good agreement with the experiment as well.However, the simulation suggests a similar response in both of the blue probe beams,which is contrary to the experiment. The signals in the 488 nm probe beam werealways stronger than the signals at 405 nm.

The increasing signal amplitude with respect to the excitation fluence can be ex-plained by the expansion of the vapour bubble. If the steam layer around the par-ticle is too thin, the goldsphere can still “feel” the surrounding water by means of

26


(b) 80 nm gold particles in water

(a) 50 nm goldparticles in water

400 450 500 550 600 650 7000.00

0.25

0.50

0.75

1.00 20°C in water gold at 300°C in vacuum melted gold at

1064°C in vacuum

optde

nsity

[a.u

.]

wavelength [nm]

400 450 500 550 600 650 7000.00

0.25

0.50

0.75

1.00 20°C in water gold at 300°C in vacuum melted gold at

1064°C in vacuum

optde

nsity

[a.u

.]

wavelength [nm]

400 500 600 700

-0.8

-0.6

-0.4

-0.2

0.0

Dop

t.de

nsity

[a.u

.]

wavelength [nm]

405nm

488mn

561mn

635nm660nm

400 500 600 700

-0.8

-0.6

-0.4

-0.2

0.0

Dop

t.de

nsity

[a.u

.]

wavelength [nm]

405nm

488mn

561mn

635nm660nm

Figure 4.8: Simulated spectra for heated particles at 300 ◦C surrounded by vacuum (left)and the corresponding signal changes. The vertical lines indicate the wavelengths of theprobe lasers.

an effective refractive index larger than one. Only if the bubble is large enough, theeffect of the surrounding water can be neglected. This might account for the bendsthat can be seen in the signal amplitude vs. laser fluence diagram (Fig. 4.7 (b)).MiePlot only offers simulations for a sphere embedded in an infinite medium, the ex-act core-shell problem being difficult to calculate. In section 2.1.4(b) in [Kre95] thesituation of a spherical hetero-system is discussed. According to their calculations, anadditional dielectric layer covering a sodium cluster leads to a shift of the resonance,which depends on the layer thickness. In the limit of large thickness, the spectrumcorresponds to the case of a sodium cluster embedded in the pure dielectric.

27


The formation of a vapour layer leads to a heat confinement in the particle. If thishappens during the laser pulse, the heating of the particle will be accelerated andeventually it will reach its melting temperature (TAum = 1064 ◦C). The impact ofparticle melting on the optical properties have also been simulated with MiePlot(dashed line in Fig. 4.8). It shows that the plasmon peak disappears completelyfrom the extinction spectrum. Compared to the hot solid particle, the extinction isfurther decreased in the blue and increased in the red spectral range. This is in goodagreement with the results from Fig. 4.7.

The melting of the particle does not necessarily have to be the last step. The offsetin the static extinction signal after the excitation in 635 nm (Fig. 4.6 (b)) indicatesirreversible changes in the particle itself. The internal temperatures can easily reachthe boiling point of the gold (TAub = 2856 ◦C). However, the static extinction spec-tra recorded after the experiments did not indicate dramatic changes following theirradiation in the medium fluence regime.

4.4 The high fluence regime

4.4.1 Results

With the advanced setup (expanded beam and thin glass cells) the maximum laserfluence was limited to the medium fluence regime. In previous studies with an unex-panded Nd:YAG beam and with 10 mm glass cells it was possible to generate anotherclass of signals at even higher fluences. Unfortunately, in this state of the experi-ments the energy calibration was not yet performed by means of laser fluence at theprobe volume. Only absolute pulse energies were recorded. However, this dependencyshould be more or less comparable to the last studies and therefore the logarithmicfit function (cp. Fig. 3.3 on page 17) was used to convert the pulse energy. Thesevalues should be proportional to the average laser fluence at the probe volume (hencethe “a.u.” at the fluence axis).

At a certain fluence the extinction drop observed in the medium fluence regimewas superimposed by another peak in the positive direction of some nanosecondsduration (see Fig. 4.9). The analysis of the peak heights in Fig. 4.10 shows thatthe amplitude keeps growing towards higher excitation fluences with the response inthe blue probe signals being stronger than in the red ones. Eventually the samplebecomes completely opaque (i.e. optical density > 200 m−1; higher values for ODcould not be resolved in the setup). For the 80 nm particle samples even a differentthreshold for the onset of the signals was observed for blue and red wavelengths.

Again, the red probe signals revealed irreversible changes in the extinction signals.They were stable for several milliseconds and a bright spot could be seen in the cells

28


(b)(a)

0 20 40 60 80 100 120 140 160 180 200

0

5

10 0 20 40 60 80 100 120 140 160 180 200

0

5

100 20 40 60 80 100 120 140 160 180 200

-10-505

1015

0 20 40 60 80 100 120 140 160 180 200-10-505

1015

time [ns]

Dop

t.de

nstit

y[m

-1]

660nm

488nm

405nm

635nm

0 20 40 60 80 100 120 140 160 180 200-10

-5

00 20 40 60 80 100 120 140 160 180 200

-10

-5

00 20 40 60 80 100 120 140 160 180 200

-10

0

10

200 20 40 60 80 100 120 140 160 180 200

-10

0

10

20

time [ns]D

opt.

dens

tity

[m-1]

660nm

488nm

405nm

635nm

Figure 4.9: Optical density signals for (a) 50 nm and (b) 80 nm particle suspensions at thehigh fluence regime. The onset of the characteristic extinction peaks in (b) for the bluewavelengths can clearly be seen, while the red probe signals only reveal smallest peaks(black arrows).

(b)(a)

0 20 40 60 80 100

0

20

40

60

80

100

120

140

160

180

max

Dop

t.de

nstit

y[m

-1]

405nm 488nm 635nm 660nm

laser fluence [a.u.]

0 20 40 60 80

0

10

20

30

40

50

60

max

Dop

t.de

nstit

y[m

-1]

660nm 635nm 488nm 405nm

laser fluence [a.u.]

Figure 4.10: Positive peak signal as a function of excitation fluence in (a) 50 nm and (b)80 nm goldparticle suspensions. Optical densities above 200 m−1 correspond to a nearlycompletely opaque sample.

even with the naked eye. It indicates a permanent damage of the nanospheres fol-lowing the laser irradiation, which is corroborated by the extinction spectra recordedafter the experiment. Fig. 4.11 shows the effect of the experiments at high fluenceexcitation on the spectra of the particle suspensions.

In order to avoid the accumulation of the effect on subsequent excitations, the sus-pensions were stirred after every irradiation.

29


400 450 500 550 600 650 7000

20

40

60

80

100

opt.

dens

ity[m

-1]

before after

irradiation

wavelength [nm]

400 450 500 550 600 650 7000

20

40

60

80

100

120

140

opt.

dens

ity[m

-1]

before after

wavelength [nm]

(a) (b)

Figure 4.11: Irreversible changes by high fluence irradiation on 50 nm (a) and 80 nmparticle suspensions. The blueshift of the peak position in indicates a reduction of theaverage particle size.

A last interesting effect can be seen in Fig. 4.12, where the extinction signals inthe red wavelengths show an additional drop with a duration of roughly 5 ns. Thetimescale of this drop does not change with higher excitation fluences and the signaldoes not disappear from the photodiodes if the probe lasers are turned off.

0 20 40 60 80 100-4

-2

0

0 20 40 60 80 100-4

-2

0

time [ns]

Dop

t.de

nstit

y[m

-1]

635nm

660nm

Figure 4.12: At a certain flu-ence, a 5 ns signal appearsthat does not vanish whenthe probe lasers are switchedoff. The signals depictedhere were recorded at a flu-ence of 57 mJ/cm2 (pulse en-ergy 50 mJ).

4.4.2 Discussion

The effects that have been presented in the previous sections could all be explainedby the impacts of heating and evaporation of the surrounding water on the opticalproperties of the goldparticle. However, the scattering behaviour of the bubbles has

30


been neglected so far. Fig. 4.13 shows the Mie-simulation of the extinction crosssection for a steambubble as a function of its diameter for four probe wavelengthsand compares it to the peak extinction cross section of an undisturbed gold particleof 50 and 80 nm diameter. The plot shows two important aspects of the problem:First, the scattering of the vapour bubbles can be neglected completely, as long asthe bubbles have diameters below 100− 150 nm. Second, the shorter wavelengths aremore sensitive to bubble scattering. Hence, the signals in Fig. 4.10 clearly show thescattering behaviour that would be expected from gasbubbles in water.

Figure 4.13: Simulated extinc-tion cross section for an airbub-ble in water and for comparisonthe peak extinction cross sec-tion of 50 nm and 80 nm gold-spheres (horizontal lines). Thescattering of bubbles with di-ameters below 100 nm is negli-gible. It turns out that shorterwavelengths are more sensitiveto bubbles.

0 100 200 300 4000.00

0.02

0.04

660nm 635nm 488nm 405nm peak ext. 50nm Au peak ext. 80nm Au

extin

ctio

ncr

oss

sect

ion

[mm

2 ]

bubble diameter [nm]

The signals emerging in the red wavelengths (Fig. 4.12) could be interpreted eitheras thermal radiation or as luminescence of the gold. According to the estimationfrom Sec. 2.2.2, page 9, the surface of the goldparticles emits a power of 1.4 MW/m2

at a temperature of 3000 K. In the volume, that is irradiated by the laser (spotdiameter: 5 mm, layer thickness: 2 mm, particle concentration: ∼ 10−16 m−3), thereare roughly 4 · 106 particles with an overall surface area of 8 · 10−8 m2 (spheres withdiameter 80 nm). Hence, the power of the blackbody radiation from these particlesis 110 mW. The distance between the sample and the photodiodes is one meter. Theprobe lasers are focussed onto the photodiodes by a lens (area ∼ 1 cm2), so only afraction of 10−5 or 1 µW reaches the photodiode. However, the peak power of thesignals can be estimated to 1− 2 mW. Therefore, thermal radiation as the origin ofthe signal can be ruled out.

The quantum efficiency of photoluminescence (cp. Sec. 2.2.2, page 9) is reported tobe in the order of 0.01% to 0.1% [Wil98]. At the appearance of the signals, the pulseenergy approximately 50 mJ. At a wavelength of 532 nm, ∼ 35% of the energy isabsorbed2 by the particles. With a quantum efficiency of 0.1% and a pulse duration

2The transmittance of a 2 mm layer at 532 nm of the goldparticle suspension is 40% (see Fig. 4.2 onpage 21); about 40% of the extinction can be ascribed to elastic scattering.

31


of 10 ns, the power of the luminescence radiation at the sample would be 180 W or1.8 mW at the photodiode, which is very close to the observed effect.

If the signals are caused by luminescence, they will have a characteristic spectrum inthe red and infrared spectral range [Bev03]. A first indication towards a broadbandcharacter of the signals is that they could only be observed, when the photodiodesfor the red probe beams were equipped with an edge filter (i.e. all wavelengths belowa certain value, 600 nm in this case, are blocked). The signals disappeared when anadditional narrowband interference filter was used.

4.5 Experiments with uv-excitation and a yellow

probe laser

The results and their interpretation from the previous sections have demonstratedthe complex correlation of local temperature distribution and the optical propertiesof gold nanoparticles. It turned out that the plasmon resonance wavelength is alreadyshifted during the excitation pulse. The wavelength of 532 nm was initially chosento ensure a sufficiently high absorption in the sample. However, this absorptionis not constant during the laserpulse. Thus, the excitation should be performedin a spectral range, where the absorption is less affected by temperature changes.The third harmonic of the Nd:YAG laser has a wavelength of 355 nm, which is inthe rather stable interband absorption regime of the gold spectrum. Moreover, thesimulations in Fig. 4.5 and 4.8 have shown, that the laser-induced shifts are mostprominent in the spectral range between 500 and 600 nm. These considerations ledto the implementation of a last experiment with a frequency-tripled Nd:YAG and anadditional probelaser at a wavelength of 561 nm. First results on 80 nm goldparticlesuspensions are displayed in Fig. 4.14. They are still lacking an appropriate energycalibration, hence the graphs are labelled with the pulse energy of the reflection of aglass slide in the Nd:YAG-beam (cp. Fig. 3.1 on page 16).

A main result of this study is an enormous boost in sensitivity due to the use of the561 nm probe laser. It clearly corroborates the simulations from Fig. 4.5 and Fig.4.8. The characteristic signals from the low and the medium fluence regimes could bereproduced. The transition between the two regimes is clearly visible in 4.14(b) (blackarrow). The longer relaxation times for the signal at 405 nm, observed in 4.6 on page25, could not be reproduced. Finally, at the highest excitation powers, the transitionto bubble-dominated extinction was observed. Again, the short wavelengths showeda stronger response than the longwave signals.

32

4.5 Experiments with uv-excitation and a yellow probe laser

0 20 40 60 80 100 120 140 160 180 200-6-4-20

0 20 40 60 80 100 120 140 160 180 200-25-20-15-10-50

0 20 40 60 80 100 120 140 160 180 200-1

0

1

20 20 40 60 80 100 120 140 160 180 200

-10

-5

0

time [ns]

Dop

t.de

nstit

y[m

-1]

635nm

30 µJ

488nm

405nm

561nm

0 20 40 60 80 100 120 140 160 180 200

-20246 0 20 40 60 80 100 120 140 160 180 200

-20-15-10-50

0 20 40 60 80 100 120 140 160 180 200-10

-5

0

0 20 40 60 80 100 120 140 160 180 200-10-505

10

time [ns]

Dop

t.de

nstit

y[m

-1]

635nm

57 µJ

488nm

405nm

561nm

(a) (b)

(c) (d)

0 20 40 60 80 100 120 140 160 180 200

-4

-2

00 20 40 60 80 100 120 140 160 180 200

-30-20-10

00 20 40 60 80 100 120 140 160 180 200

-4-202

0 20 40 60 80 100 120 140 160 180 200

-10

-5

0

time [ns]

Dop

t.de

nstit

y[m

-1]

635nm

47 mJ/cm²

488nm

405nm

561nm

0 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-3-2-10

0 20 40 60 80 100 120 140 160 180 200

-1

0

10 20 40 60 80 100 120 140 160 180 200

-2

0

2

time [ns]

Dop

t.de

nstit

y[m

-1]

635nm

8 µJ

488nm

405nm

561nm

Figure 4.14: First results of experiments performed with uv-excitation on 80 nm goldpar-ticle suspensions and a 561 nm probe laser. The main features of the previous studiescan be reproduced: the low fluence (a) and medium fluence (b) regime and the transi-tion between them (c). Furthermore the signals at high excitation energies shows thecharacteristic bubble dominated scattering behaviour of the high fluence regime (d).

33

5 Outlook

From the results of the time resolved extinction measurements a detailed mechanismfor the dissipation of a nanosecond laserpulse could be inferred. However there arestill many open questions regarding experimental issues and the interpretation of thesignals.

Theoretical questions

� With the Mie theory the signals were interpreted qualitatively. However thequantitative response cannot be explained by a simple combination of temper-ature dependent bulk dielectric functions of medium and sphere. The waterpressure at the surface of the particle, especially when the bubble nucleationsets in, will also play an important role. With the formation of a vapour layeraround the particle, the system acts like a core-shell system, which is even moredifficult to model.

� The dynamics of the heat transfer upon nanosecond heating have not beensimulated satisfactorily, so far. Especially the time dependent absorption duringthe laser pulse will be difficult to take into account. A possible approach wouldbe to extend the algorithm of Jorg Bischof (see [Bis96] and Appendix C) toa spherical symmetric situation, e.g. by an increasing heat capacity of layers,that are further away from the centre of the particle.

Experimental tasks

� The first experiments with an excitation wavelength of 355 nm have providedcomparable results to the previous studies at 532 nm. Compared to the plasmondominated green spectral range, the ultraviolet optical properties of the goldnanoparticles are dominated by interband absorption. Hence, they are lessaffected by the temperature changes during the excitation pulse. Comparisonwith simulations assuming a constant absorption rate for the pulsed laser, thatare easier to implement, would be possible.

� A very important issue for the comparability of the results is the energycalibration. The setup for the uv excitation still lacks an appropriate cali-

35

5 Outlook

bration measurement. Furthermore, the method with the pinhole should becompared with other methods, such as the melting dynamics of a germaniumsurface1 [Bon93].

� The strongest relative extinction changes are expected in the green and yellowspectral range. With an excitation wavelength in the ultraviolet it is now pos-sible to study the optical properties in that particular range. First experimentswith a 561 nm probelaser already demonstrated an immense boost in sensitivity.Another alternative would be a continuous wave Nd:YAG at 532 nm.

� As a result of the heating, the Mie calculation for the low fluence regime pre-dicted an increased extinction for the 80 nm goldparticles in the spectral rangefrom 485 nm up to 518 nm (cp. Fig. 4.5 on page 24) in contrast to an extinctiondrop for all other visible wavelengths. The emission of the argon-ion laser can beadjusted to different wavelengths in that range (476.5 nm, 488.0 nm, 496.5 nm,501.7 nm, 514.5 nm and 528.7 nm). Using these wavelengths, the predictions ofthe Mie theory can be tested.

� The influence of the particle size on the nanoscale heat transfer propertieswould be another parameter worth studying. Changing the particle materialcould bear some experimental problems, viz. the nonexistence of a plasmonresonance in the visual spectral range.

� The experiments have shown that the plasmon resonance is very sensitive tochanges in the particle and its environment. Hence, the time resolved extinc-tion of gold nanoparticle suspensions acts like a thermometer for the nanoscaleheat transfer. With an appropriate theoretical model it is possible to controlthe thermodynamic conditions both in and around the particle. An interestingapplication would be to use goldparticles as microreactors. At controlled tem-peratures, chemical reactions or phase transitions in surface bound molecularlayers could be stimulated.

1The threshold fluence for surface melting of germanium at ns-illumination is 100 mJ/cm2, which isat the upper end of the fluence scale for the measurements in Sec. 4.3

36

Summary

For the first time in this group, bubble nucleation was studied at nanoscopic inter-faces, namely on the surface of gold nanoparticles suspended in water. Their plas-monic properties proved to be a very sensitive indicator for dielectric modificationsboth in and around the particles. By probing at four wavelengths simultaneously, theimpact of an excitation by a pulsed laser on the optical properties could be studiedclose to the plasmon resonance (488 nm, 561 nm1 and 635 nm) as well as in the in-terband absorption regime (405 nm) and the longwave shoulder of the plasmon peak(660 nm). From the comparison of the time-resolved extinction measurements on50 nm and 80 nm goldparticle suspensions with Mie simulations including the tem-perature dependent bulk dielectric functions of both the particle and matrix material,the mechanism of bubble nucleation around the particles could be inferred.

Already moderate excitation powers give rise to changes in the absorbance of thesamples, which are being ascribed to changes in the optical properties caused by theheating of the particle and its environment (low fluence regime). The formation of avapour layer around the particle at higher excitation fluences leads to a decoupling ofthe plasmonic oscillations in the electron gas of the particle from the dielectric of thesurrounding water layers (medium fluence regime). This results in a extinction dropin the whole visible spectral range. The formation of the bubble at a certain thresholdfluence is clearly visible in the signal of the 488 nm probe laser, where the responseascribed to the heating (an extinction increase) is complementary to the extinctiondrop due to the bubble. With increasing excitation fluence, the bubbles becomelarger and eventually, the scattering properties of the bubbles become dominant.The extinction at this high fluence regime clearly reflects the scattering behaviourthat would be expected from vapour bubbles, viz. a stronger scattering in shorterwavelengths. Finally the sample became completely opaque for some nanoseconds,showing an Optical Limiting behaviour.

A first experiment demonstrated that the sensitivity of the setup can be increasedby utilizing probe wavelengths closer to the plasmon peak. Furthermore, the excita-tion wavelength was shifted to the ultraviolet, where the absorption is more stablethroughout the laser pulse. The main features of the previous studies could be re-produced. Moreover, the prediction by the Mie theory of a highly increased opticalresponse in the green and yellow spectral rage was corroborated.

1With the 561 nm laser only one last experiment was performed (see Sec. 4.5).

37

Appendix A

Mie theory

In this section the basic ideas of the Mie theory are introduced. The descriptionfollows the notation of [Boh83], where the complete derivations can be found.

The first step is to describe the incoming electromagnetic wave in spheric coordinateswith the sphere placed in the origin. The electric field can be described by

~Ei(r, ϑ, ϕ) = E0

∞∑n=1

in2n+ 1

n(n+ 1)(~

M(1)n (r, ϑ, ϕ)− i ~N (1)

n (r, ϑ, ϕ)). (A.1)

The vector functions M(0)n (r, ϑ, ϕ) and

~N

(0)n (r, ϑ, ϕ) are called vector spherical har-

monics. They have to be chosen in a way that they satisfy the electromagneticwave equation. They turn out to have the form {trigonometric function} · {sphericalBessel function} · {Legendre function}. The corresponding magnetic fields Hi can bederived from (A.1) using the Maxwell equations. At the surface of the sphere, theboudary condition has to be fulfilled :

( ~Ei + ~Es − ~Eint)× ~er = ( ~Hi + ~Hs − ~Hint)× ~er = 0 (A.2)

The indices i, s and int stand for the incident, the scattered and the internal fields,respectively. They can be described in the form

~Eint = E0

∞∑n=1

in2n+ 1

n(n+ 1)(cn

~M

(1)n − idn ~

N(1)n ), (A.3a)

~Hint =−kintωµint

∞∑n=1

, in2n+ 1

n(n+ 1)(dn

~M

(1)n − icn ~

N(1)n ), (A.3b)

~Es = E0

∞∑n=1

in2n+ 1

n(n+ 1)(ian

~N

(0)n − bn ~

M(3)n ), (A.3c)

~Hs =−kωµ

∞∑n=1

in2n+ 1

n(n+ 1)(ian

~N

(0)n − bn ~

M(3)n ), (A.3d)

39

Appendix A Mie theory

where kint and k are the wavenumbers and µint and µ the permeabilities1 inside andoutside the sphere, respectively. The spherical harmonics are multiplied with complexfunctions an, bn, cn and dn called scattering coefficients. The functions cn and dn areof no further interest, as they only describe the internal field of the particle. Theother coefficients are found to be

an =mΨn(mx)ψ′n(x)−Ψn(x)ψ′n(mx)

mΨn(mx)ξ′n(x)− ξn(x)ψ′n(mx)(A.4a)

bn =Ψn(mx)ψ′n(x)−mΨn(x)ψ′n(mx)

Ψn(mx)ξ′n(x)−mξn(x)ψ′n(mx), (A.4b)

with the relative refractive index m = n0(ω)/nm, the ratio of the frequency depen-dent refractive index of the sphere to the refractive index of the surrounding mediumand the size parameter x = 2π

λR nm, where R denotes the particle radius. The

Riccati-Bessel functions ψ′n(x) = xjn(x) and ξ′n(x) = xhn(x) are derived from thespheric Bessel function of first kind jn(x) and third kind hn(x), respectively. With ψ′

the first derivative with respect to the whole argument in parentheses is meant. Inorder to get information about how much energy is taken from the incident planarwave, the Poynting vector ~S = ~E × ~H of the resulting electromagnetic field has tobe integrated over a closed surface around the sphere, which is sufficiently far awayin order to avoid near field effects:

W = −∮~S ·~n dA. (A.5)

~n is the outward pointing surface normal vector (hence the ”-” sign). The resulting

Poynting vector can be written as ~S = ~Si + ~Ssca + ~Sext, where ~Si and ~Ssca are thecomponents of the incident and scattered wave. ~Ssca contains the mixed terms andcan be interpreted as the total energy loss of the incident wave after the particle(ext for extinction). Furthermore, the energy flux of a planar wave through a closedsurface will be zero. Hence the contribution of the undisturbed incident wave will bezero. This leads to the equation for the nonradiative energy loss:

Wabs = Wext −Wsca. (A.6)

1Usually they are assumed to be unity for optical frequencies.

40

The corresponding cross sections can be obtained by normalizing the different con-tributions by the irradiance Ii of the incident field (dimensions: energy per area andtime):

σsca =Wsca

Ii=

2π

k2

∞∑n=1

(2n+ 1)(|an|2 + |bn|2

)(A.7a)

σext =Wext

Ii=

2π

k2

∞∑n=1

(2n+ 1)Re {an + bn} (A.7b)

These equations are the basis for the calculation of the extinction spectra as they areused in this work. Additionally, the dielectric functions of the sphere material andthe medium are required (bulk values are sufficient; see discussion in chapter 2.1.2).For every frequency ω the scattering cefficients (A.4) of the first significant ordersare computed. Here the size parameter x = 2π

λR nm can act as a stop criterion: for

n > x the contributions become negligible. An example for a complete computationalgorithm is the BHMIE - algorithm, which is used in the freeware software MiePlot[Lav06]. It is decribed in Chapter 4 and Appendix A of [Boh83].

41

Appendix B

Temperature dependent opticalconstants of gold

The Mie-simulation software MiePlot [Lav06] requires the wavelength dependentcomplex refractive indices of the particle material. The standard source for the op-tical constants of noble metals is a paper by Johnson and Christy [Joh72]. However,they only studied gold at room temperature. For temperature dependent values thedata from Otter [Ott61] can be used. Unfortunately, the data is only availlable inthe form a single plot (Fig. B.1). The relations between dielectric constants ε1 andε2 and the complex refractive indices n and k are given by

ε1 + iε2 = (n+ ik)2 (B.1)

⇒ k =

√1

2

(√ε21 + ε22 − ε1

)(B.2)

⇒ n =ε22k

(B.3)

The following tables will give both the dielectric constants and the corresponding re-fractive indices for wavelengths between 440 nm and 640 nm from the plot. Additionalvalues for 400 nm and 700 nm have been extrapolated in order to get information forthe probelaser wavelengths at 405 nm and 660 nm.

43

Appendix B Temperature dependent optical constants of gold

wavelength [nm] −ε1 ε2 n k

400 1,1* 6,8* 1,7* 2*

440 1,12 6 1,58 1,9

460 1,31 5,45 1,47 1,86

480 1,84 4,57 1,24 1,84

500 2,76 3,69 0,96 1,92

520 4,08 2,94 0,69 2,13

540 5,52 2,47 0,51 2,4

560 7,69 2,16 0,39 2,8

580 8,62 1,95 0,33 2,95

600 10 1,74 0,27 3,17

620 11,64 1,71 0,25 3,42

640 13,03 1,92 0,27 3,62

700 17,2* 2,55* 0,31* 4,16*

Table B.1: Optical constants of gold at 310 ◦C. Values with an asterisk are extrapolated.


400 0,5* 7,5* 1,87* 2*

440 1,31* 6,8* 1,68* 2,03*

460 1,84* 6,25* 1,53* 2,04*

480 2,36 5,8 1,4 2,08

500 3,2 5,01 1,17 2,14

520 4,08 4,62 1,02 2,26

540 5,07 4,05 0,84 2,4

560 6,7 3,82 0,71 2,68

580 7,9 3,56 0,62 2,88

600 9,5 3,4 0,54 3,13

620 10,52 3,3 0,5 3,28

640 11,8* 3,25* 0,47* 3,47*

700 15,64* 3,1* 0,39* 3,97*

Table B.2: Optical constants of solid gold at the melting point of 1064 ◦C. Values withan asterisk are extrapolated.

44


400 0,5* 7,69* 1,96* 1,96*

440 1,84* 6,88* 1,85* 1,85*

460 2,5* 6,77* 1,84* 1,84*

480 3,42 6,66 1,82 1,82

500 4,21 6,55 1,81 1,81

520 5 6,44 1,79 1,79

540 5,92 6,33 1,78 1,78

560 6,71 6,22 1,76 1,76

580 7,63 6,13 1,75 1,75

600 8,82 6,13 1,75 1,75

620 10 6,13 1,75 1,75

640 11,31* 6,13* 1,75* 1,75*

700 15,24* 6,13* 1,75* 1,75*

Table B.3: Optical constants of liquid gold at the melting point of 1064 ◦C. Values withan asterisk are extrapolated.

Figure B.1: Graph from [Ott61].The plots show the dielectric con-stants for different temperatures:−ε1 (upper graph) and ε2 (lowergraph).

544 M. O ~ R :

Auch die Polarisation beider Metalle weist in dem sichtbaren Spektral- bereich X-Punkte auf. Der im Bereich der freien Elektronen negative Temperaturkoeffizient wird im Bereich der Absorptionskante positiv mit X-Punkten bei etwa 0,60 ~ im Falle des Cu und bei 0,52 ~z bei Au. Bei noch ktirzeren Wellen verschwindet der Temperaturkoeffizient aber- mals, m6glicherweise um wieder das Vorzeichen zu wechseln. ]3ei Cu

75

,lf 2-n 2

70

2nk

8

o 7a~

�9 57ooc f / / - /

zoes ~ 2 ~ ' / 3

�9 qO6d ~ f l f

I I ~ I I I I I I t I

I I I t 1 I I # [ T I 0,50 0,6a I.~

Fig. 3. Temperaturverhaltelz der optischen Konstanten voi1 Au im sichtbaren Spektralbereich

sinkt sein Wert nnterhalb von 0,50 a unter die MeBgenauigkeit. Bei Au liegt ein zweiter X-Punkt der Polarisation bei 0,44 ~. Es sei hervor- gehoben, dab die Messungen die Existenz anch mehrerer X-Punkte ergeben und dab die X-Punkte verschiedener optischer Eigenschaften eines Metalls bei verschiedenen Wellenl~ingen liegen k6nnen.

Die beiden MeBkurven, die jeweils die spektralen optischen Eigen- schaften des festen und geschmolzenen Metalls bei der Schmelztempe- ratur darstellen, zeigen deutlich, dab bei beiden Metallen die Absorption und bei Au auch die Polarisation sich beim Schmelzen unstetig ~tndern. Sehr augenf~llig wird diese Anderung auch durch den Unterschied in der Farbe des yon der festen und der fltissigen Phase emittierten Lichtes. Dieser Tatsache ist es ja auch zu danken, dab man beim Ztichten der

45

Appendix C

One dimensional heat transfer

Three dimensional heat transfer, even in spherically symmetric geometry, is very diffi-cult to simulate. Unfortunately no analytical solution to the problem has been foundso far. A half analytical solution was proposed by Goldenberg [Gol52] and Cooper[Coo77]. A big effort has been carried out towards numerical solutions. However,even applying these formula to rectangular heating pulse is very time consuming, notto mention a gaussian pulse profile.

Within the scope of his dissertation Jorg Bischof developed a software for the simula-tion of the one dimensional heat transfer from a laser illuminated surface [Bis96]. Itutilizes the method of finite differences, where the system is split in a finite numberof layers with defined thermodynamic properties. For interfaces between differentmaterials, the thermal boundary resistance can be included. Of course, in the onedimensional case plasmonic contributions to the absorption in the film are neglected.The timescales from these simulations can be used as a upper limit of the timescalethe three dimensional problem. In Fig. C.2 the simulation of the temperature inand around a 80 nm thick gold film surrounded by water is shown. For the thermalboundary resistance of the water-gold interface a value of 100 MJ/m2K was used[Ple04, Wil02]. The excitation source was a 532 nm, 9 ns FWHM light pulse at apower of 50 mJ/cm2. The initial temperature was set to room temperature (293 K).

The decay times for the temperature are in the order of 100− 150 ns. The peaktemperature is reached with a little delay to the peak of the excitation pulse, whichis prolongated for more distant water layers. A residual temperature increase of10− 20 K remaines for at least 500 ns.

47

Appendix C One dimensional heat transfer

0 100 200 300 400 500

300

320

340

360

380

tem

pera

ture

[K]

time [ns]

Temperature evolution inside the goldfilm 5nm from the surface 25nm from the surface 50nm from the surface Nd:YAG pulse

Figure C.1: Simulated heat transfer from a 80 nm gold film to the surrounding waterlayers.

0 20 40 60 80

300

320

340

360

380

tem

pera

ture

[K]

time [ns]

Temperature evolution inside the goldfilm 5nm from the surface 25nm from the surface 50nm from the surface Nd:YAG pulse

Figure C.2: Detail of the first 80 ns of the simulated heat transfer.

48

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Acknowledgements

Der englischsprachige Leser wird es mir verzeihen, dass ich die Danksagungen inmeiner Muttersprache verfasse. Viele Menschen verdienen an dieser Stelle einenbesonderen Dank:

� Prof. Dr. Johannes Boneberg, ohne dessen engagierte und fachkundige Betreu-ung mit zahllosen Diskussionen, fachspezifisch wie fachfremd, mir die Arbeitnur halb soviel Spaß bereitet hatte,

� Prof. Dr. Paul Leiderer, der sehr viel Wert auf eine angenehme Arbeitsathmo-sphare an seinem Lehrstuhl legt und seine Mitarbeiter mit trickreichen Fragenimmer wieder zu Hostleistungen anspornt,

� Prof. Dr. Thomas Dekorsy fur die Ubernahme des Zweitgutachtens,

� Dr. Anton Plech, ein wahrer Experte auf dem Gebiet der Plasmonen, ohnedessen Ratschlage meine Arbeit in dieser Form gar nicht moglich gewesen ware,

� der gesamten “Diplozimmer”-Crew, besonders aber Andreas Kolloch undStephen Riedel furs Korrekturlesen,

� Louis Kukk, der mich jetzt hoffentlich doch nicht als Lehrling in seinerFeinmechanik-Werkstatt anstellen muss, fur diverse Details und Anregungenrund um meinen Aufbau,

� den “Doktos”, die in Notfallen auch abends und am Wochenende unter “2627”erreichbar sind,

� Regina Bauer, dass sie fur mich da ist wenn ich sie brauche,

� meinen Eltern, deren Unterstutzung mir schon immer sehr viel bedeutet hat.

laserinduced nanobubbles - mpip-mainz.mpg.dewebers/pdf/diploma_thesis_stefanweber.… ·...

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